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All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Staggered solution procedures for multibody dynamics simulation

The numerical solution procedure for multibody dynamics (MBD) systems is termed a staggered MBD solution procedure that solves the generalized coordinates in a separate module from that for the constraint force. This requires a reformulation of the constraint conditions so that the constraint forces can also be integrated in time. A major advantage of such a partitioned solution procedure is that additional analysis capabilities such as active controller and design optimization modules can be easily interfaced without embedding them into a monolithic program. After introducing the basic equations of motion for MBD system in the second section, Section 3 briefly reviews some constraint handling techniques and introduces the staggered stabilized technique for the solution of the constraint forces as independent variables. The numerical direct time integration of the equations of motion is described in Section 4. As accurate damping treatment is important for the dynamics of space structures, we have employed the central difference method and the mid-point form of the trapezoidal rule since they engender no numerical damping. This is in contrast to the current practice in dynamic simulations of ground vehicles by employing a set of backward difference formulas. First, the equations of motion are partitioned according to the translational and the rotational coordinates. This sets the stage for an efficient treatment of the rotational motions via the singularity-free Euler parameters. The resulting partitioned equations of motion are then integrated via a two-stage explicit stabilized algorithm for updating both the translational coordinates and angular velocities. Once the angular velocities are obtained, the angular orientations are updated via the mid-point implicit formula employing the Euler parameters. When the two algorithms, namely, the two-stage explicit algorithm for the generalized coordinates and the implicit staggered procedure for the constraint Lagrange multipliers, are brought together in a staggered manner, they constitute a staggered explicit-implicit procedure which is summarized in Section 5. Section 6 presents some example problems and discussions concerning several salient features of the staggered MBD solution procedure are offered in Section 7.

Park, K. C.↗
NASA NTRS1994

A grid generation and flow solution method for the Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a National Advisory Committee for Aeronautics (NACA) 0012 airfoil as well as a two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed.

Anderson, W. Kyle↗
NASA NTRS1994

Electron transport and energy degradation in the ionosphere: Evaluation of the numerical solution, comparison with laboratory experiments and auroral observations

Auroral electron transport calculations are a critical part of auroral models. We evaluate a numerical solution to the transport and energy degradation problem. The numerical solution is verified by reproducing simplified problems to which analytic solutions exist, internal self-consistency tests, comparison with laboratory experiments of electron beams penetrating a collision chamber, and by comparison with auroral observations, particularly the emission ratio of the N2 second positive to N2(+) first negative emissions. Our numerical solutions agree with range measurements in collision chambers. The calculated N(2)2P to N2(+)1N emission ratio is independent of the spectral characteristics of the incident electrons, and agrees with the value observed in aurora. Using different sets of energy loss cross sections and different functions to describe the energy distribution of secondary electrons that emerge from ionization collisions, we discuss the uncertainties of the solutions to the electron transport equation resulting from the uncertainties of these input parameters.

Lummerzheim, D.↗
NASA NTRS1992

Least-squares finite element solution of 3D incompressible Navier-Stokes problems

Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.

Jiang, Bo-Nan↗
NASA NTRS1995

Optical diagnostics of solution crystal growth

Solution crystal growth monitoring of LAP/TGS crystals by various optical diagnostics systems, such as conventional and Mach-Zehnder (M-Z) interferometers, optical heterodyne technique, and ellipsometry, is under development. The study of the dynamics of the crystal growth process requires a detailed knowledge of crystal growth rate and the concentration gradient near growing crystals in aqueous solution. Crystal growth rate can be measured using conventional interferometry. Laser beam reflections from the crystal front as well as the back surface interfere with each other, and the fringe shift due to the growing crystal yields information about the growth rate. Our preliminary results indicate a growth rate of 6 A/sec for LAP crystals grown from solution. Single wavelength M-Z interferometry is in use to calculate the concentration gradient near the crystal. Preliminary investigation is in progress using an M-Z interferometer with 2 cm beam diameter to cover the front region of the growing crystal. In the optical heterodyne technique, phase difference between two rf signals (250 KHZ) is measured of which one is a reference signal, and the other growth signal, whose phase changes due to a change in path length as the material grows. From the phase difference the growth rate can also be calculated. Our preliminary results indicate a growth rate of 1.5 A/sec. the seed and solution temperatures were 26.46 C and 27.92 C respectively, and the solution was saturated at 29.0 C. an ellipsometer to measure the growth rate and interface layer is on order from JOBIN YVON, France. All these systems are arranged in such a manner that measurements can be made either sequentially or simultaneously. These techniques will be adapted for flight experiment.

Kim, Yongkee↗
NASA NTRS1995

A structured multi-block solution-adaptive mesh algorithm with mesh quality assessment

The dynamic solution adaptive grid algorithm, DSAGA3D, is extended to automatically adapt 2-D structured multi-block grids, including adaption of the block boundaries. The extension is general, requiring only input data concerning block structure, connectivity, and boundary conditions. Imbedded grid singular points are permitted, but must be prevented from moving in space. Solutions for workshop cases 1 and 2 are obtained on multi-block grids and illustrate both increased resolution of and alignment with the solution. A mesh quality assessment criteria is proposed to determine how well a given mesh resolves and aligns with the solution obtained upon it. The criteria is used to evaluate the grid quality for solutions of workshop case 6 obtained on both static and dynamically adapted grids. The results indicate that this criteria shows promise as a means of evaluating resolution.

Ingram, Clint L.↗
NASA NTRS1995

Supersonic solutions of the solar-wind equations

We re-examine the inviscid solar-wind equations with heat conduction from below, and establish a fundamentally new approach for finding stellar solutions. Although the problem is fourth order, only two independent integration constants can be assigned, since two boundary conditions that are required to specify well-behaved supersonic solutions determine the values of the other two constants. The solar-wind-model of Noble and Scarf are essentially accurate for practical purposes, but in a fundamental sense they are not self-consistent. At the supersonic level, the ratio of thermal energy to gravitational potential, (kTr/GMm)(sub s), must lie in a narrow range, between 0.4375 and about 0.40, to permit well-behaved solutions for ionized hydrogen. For a supersonic solution this ratio uniquely determines the constants A and epsilon, which in turn govern not only the escape flux and the energy flux per particle but also T'(lambda approaches 0), the temperature gradient at infinity. It is very difficult to find solutions by trial and error, without employing T'(0) as a guide to the iteration of A and epsilon, because not only must (kTr/GMm)(sub s) be chosen within the acceptable range but then either A or epsilon must be guessed with phenomenal accuracy. Otherwise the numerical integration of temperature and expansion velocity do not yield acceptable values at infinity.

Chamberlain, Joseph W.↗
NASA NTRS1996

There aren't Non-Standard Solutions for the Braid Group Representations of the QYBE Associated with 10-D Representations of SU(4)

It is well known that the quantum Yang-Baxter equations (QYBE) play an important role in various theoretical and mathematical physics, such as completely integrable system in (1 + 1)-dimensions, exactly solvable models in statistical mechanics, the quantum inverse scattering method and the conformal field theories in 2-dimensions. Recently, much remarkable progress has been made in constructing the solutions of the QYBE associated with the representations of lie algebras. It is shown that for some cases except the standard solutions, there also exist new solutions, but the others have not non-standard solutions. In this paper by employing the weight conservation and the diagrammatic techniques we show that the solution associated with the 10-D representations of SU (4) are standard alone.

Yijun, Huang↗
NASA NTRS1993

A UGO/EUTD Solution for the Scattering and Diffraction from Cubic Polynomial Strips

A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) solution is developed for the scattering and diffraction from perfectly conducting cubic polynomial strips. The new solution overcomes the difficulties of the classic GO/UTD solution near caustics and composite shadow boundaries. The approach for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the scattered field which is then reduced using a uniform asymptotic procedure. New uniform reflection, zero-curvature diffraction, and edge diffraction coefficients are derived and involve the ordinary and incomplete Airy integrals as canonical functions. Higher order effects such as double edge diffraction, edge-excited creeping waves, and whispering gallery modes are not examined in this work. The UGO/EUTD solution is very efficient and provides useful physical insight into the various scattering and diffraction processes. It is also universal in nature and can be used to effectively describe the scattered fields from flat, strictly concave or convex, and concave-convex boundaries containing edges. Its accuracy is confirmed via comparison with some reference moment method (MM) results.

Constantinides, Evagoras D.↗
NASA NTRS1996

Thermodynamic Studies of Levitated Microdroplets of Highly Supersaturated Electrolyte Solutions

Highly supersaturated electrolyte solutions are studied by employing an electrodynamic levitator trap (ELT) technique. The ELT technique involves containerless suspension of a microdroplet thus eliminating dust, dirt, and container walls which normally cause heterogeneous nucleation. This allows very high supersaturations to be achieved. A theoretical study of the experimental results obtained for the water activity in microdroplets of various electrolyte solutions is based on the development of the Cahn-Hilliard formalism for electrolyte solutions. A correspondence of 96-99% between the theory and experiment for the all solutions studied was achieved and allowed the determination of an analytical expression for the spinodal concentration n(sub spin) and its calculation for various electrolyte solutions at 298 K.

Myerson, Allan S.↗
NASA NTRS1999

Step Bunching: Influence of Impurities and Solution Flow

Step bunching results in striations even at relatively early stages of its development and in inclusions of mother liquor at the later stages. Therefore, eliminating step bunching is crucial for high crystal perfection. At least 5 major effects causing and influencing step bunching are known: (1) Basic morphological instability of stepped interfaces. It is caused by concentration gradient in the solution normal to the face and by the redistribution of solute tangentially to the interface which redistribution enhances occasional perturbations in step density due to various types of noise; (2) Aggravation of the above basic instability by solution flowing tangentially to the face in the same directions as the steps or stabilization of equidistant step train if these flows are antiparallel; (3) Enhanced bunching at supersaturation where step velocity v increases with relative supersaturation s much faster than linear. This v(s) dependence is believed to be associated with impurities. The impurities of which adsorption time is comparable with the time needed to deposit one lattice layer may also be responsible for bunching; (4) Very intensive solution flow stabilizes growing interface even at parallel solution and step flows; (5) Macrosteps were observed to nucleate at crystal corners and edges. Numerical simulation, assuming step-step interactions via surface diffusion also show that step bunching may be induced by random step nucleation at the facet edge and by discontinuity in the step density (a ridge) somewhere in the middle of a face. The corresponding bunching patterns produce the ones observed in experiment. The nature of step bunching generated at the corners and edges and by dislocation step sources, as well as the also relative importance and interrelations between mechanisms 1-5 is not clear, both from experimental and theoretical standpoints. Furthermore, several laws controlling the evolution of existing step bunches have been suggested, though unambiguous conclusions are still missing. Addressing these issues is the major goal of the present project. The theory addressing the above problem, experimental methods, several figures which include: (1) the spatial wave numbers at which the system is neutrally stable as a function of growth velocity for linear kinetics and supersaturation for nonlinear kinetics; (2) a schematic of the experiment of lysozyme crystal growing under conditions of natural convection; (3) fluctuations in time, t, of the normal growth rate, R(t), vicinal slope, p(t) and Fourier Spectra of R(t), discussions and conclusions are presented.

Chernov, A. A.↗
NASA NTRS1995

Interactions in Undersaturated and Supersaturated Lysozyme Solutions: Static and Dynamic Light Scattering Results

We have performed multiangle static and dynamic light scattering studies of lysozyme solutions at pH=4.7. The Rayleigh ratio R(sub g) and the collective diffusion coefficient D(sub c) were determined as function of both protein concentration c(sub p) and salt concentration c(sub s) with two different salts. At low salt concentrations, the scattering ratio K(sub c)(sub p)/R(sub theta) and diffusivity increased with protein concentration above the values for a monomeric, ideal solution. With increasing salt concentration this trend was eventually reversed. The hydrodynamic interactions of lysozyme in solution, extracted from the combination of static and dynamic scattering data, decreased significantly with increasing salt concentration. These observations reflect changes in protein interactions, in response to increased salt screening, from net repulsion to net attraction. Both salts had the same qualitative effect, but the quantitative behavior did not scale with the ionic strength of the solution. This indicates the presence of salt specific effects. At low protein concentrations, the slopes of K(sub c)(sub p)/R(sub theta) and D(sub c) vs c(sub p) were obtained. The dependence of the slopes on ionic strength was modeled using a DLVO potential for colloidal interactions of two spheres, with the net protein charge Z(sub e) and Hamaker constant A(sub H) as fitting parameters. The model reproduces the observed variations with ionic strength quite well. Independent fits to the static and dynamic data, however, led to different values of the fitting parameters. These and other shortcomings suggest that colloidal interaction models alone are insufficient to explain protein interactions in solutions.

Muschol, Martin↗
NASA NTRS1999

Wash Solution Bath Life Extension for the Space Shuttle Rocket Motor Aqueous Cleaning System

A spray-in-air aqueous cleaning system, which replaced 1,1,1 trichloroethane (TCA) vapor degreasing, is used for critical cleaning of Space Shuttle Redesigned Solid Rocket Motor (RSRM) metal parts. Small-scale testing demonstrated that the alkaline-based wash solution possesses adequate soil loading and cleaning properties. However, full-scale testing exhibited unexpected depletion of some primary components of the wash solution. Specifically, there was a significant decrease in the concentration of sodium metasilicate which forced change-out of the wash solution after eight days. Extension of wash solution bath life was necessary to ease the burden of frequent change-out on manufacturing. A laboratory study supports a depletion mechanism that is initiated by the hydrolysis of sodium tripolyphosphate (STPP) lowering the pH of the solution. The decrease in pH causes polymerization and subsequent precipitation of sodium metasilicate (SM). Further investigation showed that maintaining the pH was the key to preventing the precipitation of the sodium metasilicate. Implementation to the full scale operation demonstrated that periodic additions of potassium hydroxide (KOH) extended the useful bath life to more than four months.

Saunders, Chad↗
NASA NTRS1998

Automated pH Control of Nutrient Solution in a Hydroponic Plant Growth System

Over, the years, NASA has played an important role in providing to and the development of automated nutrient delivery and monitoring, systems for growing crops hydroponically for long term space missions. One example are the systems used in the Biomass Production Chamber (BPC) at Kennedy Space Center (KSC). The current KSC monitoring system is based on an engineering workstation using standard analog/digital input/output hardware and custom written software. The monitoring system uses completely separate sensors to provide a check of control sensor accuracy and has the ability to graphically display and store data form past experiment so that they are available for data analysis [Fortson, 1992]. In many cases, growing systems have not been fitted with the kind of automated control systems as used at KSC. The Center for Food and Environmental Systems for Human Exploration of Space (CFESH) located on the campus of Tuskegee University, has effectively grown sweetpotatoes and peanuts hydroponically for the past five years. However they have adjusted the pH electrical conductivity and volume of the hydroponic nutrient solution only manually at times when the solution was to be replenished or changed out according to its protocol (e.g. one-week, two-week, or two-day cycle). But the pH of the nutrient solution flowing through the channel is neither known nor controlled between the update, change out, or replenishment period. Thus, the pH of the nutrient solution is not held at an optimum level over the span of the plant's growth cycle. To solve this dilemma, an automated system for the control and data logging of pH data relative to sweetpotato production using the nutrient film technique (NFT) has been developed, This paper discusses a microprocessor-based system, which was designed to monitor, control, and record the pH of a nutrient solution used for growing sweetpotatoes using NFT.

Smith, B.↗
NASA NTRS2000

Does Warming a Lysozyme Solution Cook Ones Data?

Chicken egg white lysozyme has a well characterized thermally driven phase transition. Between pH 4.0 and 5.2, the transition temperature, as defined by the point where the tetragonal and orthorhombic solubility are equal, is a function of the pH, salt (precipitant) type and concentration, and most likely of the buffer concentration as well. This phase transition can be carried out with protein solution alone, prior to the initiation of the crystallization process. We have now measured the kinetics of this process and investigated its reversibility. An aliquot of a stock protein solution is held at a given temperature, and at periodic intervals used to set up batch crystallization experiments. The batch solutions were incubated at 20 C until macroscopic crystals were obtained, at which point the number of crystals in each well were counted. The transition effects increased with temperature, slowly falling off at 30 C with a half time (time to approx. 1/2 the t = 0 number of crystals) of approx. 5 hours, and an estimated half time of approx. 0.5 hours at 43 C. Further, the process was not reversible by simple cooling. After holding a lysozyme solution at 37 C (prior to addition of precipitant) for 16 hours, then cooling and holding it at 4 C, no return to the pre-warmed nucleation kinetics are observed after at least 4 weeks. Thus every thermal excursion above the phase transition point results in a further decrease in the nucleation rate of that solution, the extent being a function of the time and temperature. Orthorhombic lysozyme crystals apparently do not undergo the flow-induced growth cessation of tetragonal lysozyme crystals. We have previously shown that putting the protein in the orthorhombic form does not affect the averaged face growth kinetics, only nucleation, for tetragonal crystals. We may be able to use this differential behavior to elucidate how flow affects tile lysozyme crystal growth process.

Pusey, Marc↗
NASA NTRS2003

Magnetic Control of Solutal Buoyancy Driven Convection

Volumetric forces resulting from local density variations and gravitational acceleration cause buoyancy induced convective motion in melts and solutions. Solutal buoyancy is a result of concentration differences in an otherwise isothermal fluid. If the fluid also exhibits variations in magnetic susceptibility with concentration then convection control by external magnetic fields can be hypothesized. Magnetic control of thermal buoyancy induced convection in ferrofluids (dispersions of ferromagnetic particles in a carrier fluid) and paramagnetic fluids have been demonstrated. Here we show the nature of magnetic control of solutal buoyancy driven convection of a paramagnetic fluid, an aqueous solution of Manganese Chloride hydrate. We predict the critical magnetic field required for balancing gravitational solutal buoyancy driven convection and validate it through a simple experiment. We demonstrate that gravity driven flow can be completely reversed by a magnetic field but the exact cancellation of the flow is not possible. This is because the phenomenon is unstable. The technique can be applied to crystal growth processes in order to reduce convection and to heat exchanger devices for enhancing convection. The method can also be applied to impose a desired g-level in reduced gravity applications.

Ramachandran, N.↗
NASA NTRS1995

Dual-Code Solution Strategy for Chemically-Reacting Hypersonic Flows

A new procedure seeks to combine the thin-layer Navier-Stokes solver LAURA with the parabolized Navier-Stokes solver UPS for the aerothermodynamic solution of chemically-reacting air flow fields. The interface protocol is presented and the method is applied to two slender, blunted shapes. Both axisymmetric and three-dimensional solutions are included with surface pressure and heat transfer comparisons between the present method and previously published results. The case of Mach 25 flow over an axisymmetric six degree sphere-cone with a non-catalytic wall is considered to 100 nose radii. A stability bound on the marching step size was observed with this case and is attributed to chemistry effects resulting from the non-catalytic wall boundary condition. A second case with Mach 28 flow over a sphere-cone-cylinder-flare configuration is computed at both two and five degree angles of attack with a fully-catalytic wall. Surface pressures are seen to be within five percent with the present method compared to the baseline LAURA solution and heat transfers are within 10 percent. The effect of grid resolution is investigated in both the radial and streamwise directions. The procedure demonstrates significant, order of magnitude reductions in solution time and required memory for the three-dimensional case in comparison to an all thin-layer Navier-Stokes solution.

Wood, William A.↗
NASA NTRS2004

Steps in Solution Growth: Revised Gibbs-Thomson Law, Turbulence and Morphological Stability

Two groups of new phenomena revealed by AFM and high resolution optical interferometry on crystal faces growing from solutions will be discussed. 1. Spacing between strongly polygonized spiral steps with low less than 10(exp -2) kink density on lysozyme and K- biphtalate do not follow the Burton-cabrera-Frank theory. The critical length of the yet immobile first Short step segment adjacent to a pinning defect (dislocation, stacking fault) is many times longer than that following from the step free energy. The low-kink density steps are typical of many growth conditions and materials, including low temperature gas phase epitaxy and MBE. 2. The step bunching pattern on the approx. 1 cm long { 110) KDP face growing from the turbulent solution flow (Re (triple bonds) 10(exp 4), solution flow rate approx. 1 m/s) suggests that the step bunch height does not increase infinitely as the bunch path on the crystal face rises, as is usually observed on large KDP crystals. The mechanism controlling the maximal bunch width and height is based on the drag of the solution depleted by the step bunch down thc solution stream. It includes splitting, coagulation and interlacing of bunches

Chernov, A. A.↗